On the General Randić index of polymeric networks modelled by generalized Sierpiński graphs

2015/10/27 by Estrada-Moreno, Alejandro, Rodríguez-Velázquez, Juan A. · 2 citations
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1510.07982

Abstract

The General Randić index R_α of a simple graph G is defined as R_α(G)=∑_v_i∼ v_j (δ_iδ_j)^α, where δ_i denotes the degree of the vertex v_i. Rodríguez-Velázquez and Tomás-Andreu [MATCH Commun. Math. Comput. Chem. 74 (1) (2015) 145--160] obtained closed formulae for the Randić index R_-1/2 of Sierpiński-type polymeric networks, where the base graph is a complete graph, a triangle-free regular graph or a bipartite semiregular graph. In the present article we obtain closed formulae for the general Randić index R_α of Sierpiński-type polymeric networks, where the base graph is arbitrary.

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• Isolation number: Cartesian and lexicographic products and generalized Sierpiński graphs
• Injective (edge) colorings of generalized Sierpiński graphs

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